Answer :

Let the energy be proportional to m and c with powers p and q respectively


E mp cq


Dimensions of E = [ML2T-2]


Dimensions of m = [M]


Dimensions of c = [LT-1]


Let us assume a dimensionless constant K such that


E=Kmp cq


Dimensionally


[ML2T-2] = [M]p[LT-1] q


=[MpLqT-q]




On comparing, p=1 and q=2


So the relation between mass, speed and energy is


E=kmc2


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